Magnetic flux-to-voltage transducer based on Josephson junction arrays

ABSTRACT

A device and method for converting magnetic flux to voltage uses a linear Fraunhofer pattern of a 1D array of long Josephson junctions. The 1D array of Josephson junctions may include from 1 to 10 9  junctions formed in a planar geometry with a bridge width within the range of 4-10 μm.

RELATED APPLICATIONS

This is a divisional of application Ser. No. 14/948,169, filed Nov. 20,2015, issued as U.S. Pat. No. 10,205,081, which claims the benefit ofthe priority of U.S. Provisional Application No. 62/082,537, filed Nov.20, 2014. Each identified application is incorporated herein byreference in its entirety.

FIELD OF THE INVENTION

The present invention relates to a device for converting magnetic fluxinto a voltage, and more particularly to such a device formed usingarrays of Josephson junctions.

BACKGROUND

In conventional antennas, the received electric field component inducesa voltage in the antenna which is amplified through resonance. Aconventional antenna is referred to as “electrically small” if its sizeis less than one-quarter of the wavelength of the receivedelectromagnetic radiation for which the antenna is tuned. The utility ofthese antennas is directly related to the wavelength of theelectromagnetic radiation, the size of the antenna, and other known lossfactors.

Current techniques for direction finding of incident signals in the highfrequency (HF) band (3 to 30 MHz) require antennas that are asignificant fraction of a wavelength and which are separated by adistance comparable to a wavelength, which at 3 MHz is 100 meters whileat 30 MHz the wavelength is 10 meters. It is not feasible to deploy suchsystems on mobile platforms, such as trucks, tanks, unmanned autonomousvehicles and planes, the dimensions of which are typically smaller thanthe wavelength of interest, particularly at the low end of the HF band.

Previous research activities have demonstrated that environmentallynoise limited detection can be achieved using superconducting loopantennas, with areas of several square centimeters, when superconductingamplifiers employing Josephson junctions have been used to detect thesignal induced in the loop antenna by the incident radiation. Theleading technology involves using arrays of superconducting quantuminterference devices (SQUIDs). Such devices utilize the interferencepatterns between two junctions connected in parallel to transduce fluxinto voltage. A variety of Josephson junction based amplifierconfigurations have been examined including single SQUIDs (asuperconducting circuit containing two Josephson junctions), seriesarrays of SQUIDs, series-parallel arrays of SQUIDs, (commonly known asSuperconducting Quantum Interference Filters (SQIF), a superconductingparametric up-converter amplifier employing a large number of SQUIDinductively coupled to a superconducting transmission line, and a longJosephson junction (known as a Josephson Fluxon Anti-Fluxon Transistor(JFAT)). These configurations for Josephson junction amplifiers exhibitgain and low front-end noise over various frequency bands from DC togreater than 20 GHz.

There is an ever-increasing need for wide bandwidth receivers that arecompact in physical size and have high data throughput. An ideal systemwould have bandwidth large enough to replace multiple systems coveringdifferent frequency ranges and would reduce the size, weight and power(SWaP) requirements for operation on mobile platforms. Sensors builtfrom high temperature superconducting (HTS) electronics may be able tofill both of these requirements for realization of this need.

Referring to FIGS. 1A and 1B, a Josephson junction is the active elementof superconducting electronics formed by two superconducting electrodes2 separated by a thin normal metal or insulating barrier 4. When a phasedifference exists across the barrier, a super current will flow in theabsence of a voltage where the critical current is the maximum supercurrent sustainable by the barrier. The current in the electrodes of aJosephson junction is carried on the edges and penetrates transverselyinto the electrode a distance of the London penetration depth λ. Thisvalue is typically around 200 nm for high transition temperaturematerials. In the barrier, the current penetrates deeper into the bridgea distance known as the Josephson penetration depth λ_(J), which forordinary conditions is typically a few microns. When the bridge width W,which corresponds to the geometrical direction perpendicular to the flowof current, is comparable to or less than λ_(J), the current isdistributed evenly across the junction. Diagrammatically illustrated inFIG. 1A, these are called “short” junctions, which exhibit a magneticflux pattern described by the Sinc function (illustrated in the inset.)In contrast, if the junction width is larger than λ_(J), e.g., 2λ_(J)<W,the current is concentrated at the edges, exhibiting a triangularpattern, as shown in FIG. 1B. These junctions are known as “long”junctions and are undesirable for most SQUID applications becausesuperconducting vortices may enter the junction, generate noise, andcorrupt the voltage transfer function.

The critical current of a Josephson junction is a function of magneticfield B given by the Fourier transform of the current density. For ashort junction, a rectangular current density yields I_(C)(B)=I_(C)|SincπBA/φ₀|, where A is the area of the junction and φ₀ is the flux quantum.This is called a “Fraunhofer pattern” and is analogous to that seen inoptics for single slit diffraction in the small slit limit (slit width˜wavelength). In the case of a long junction, the Fourier transform ofthe current density (two rectangular pulses) is a triangle. This wasexperimentally confirmed by Martin et al. in a long YBCO grain boundaryjunction. This effect may be used to detect magnetic field by DC biasingthe junction above the critical current and measuring the resultingvoltage. A sensor using a single junction was demonstrated with avoltage-to-magnetic field transfer factor of 50 V/T over a range ofabout 10 μT. The transfer factor of 50 V/T is modest in comparison tointerferometers built from two junctions connected in parallel calledSQUIDs (superconducting quantum interference devices). SQUIDs typicallyachieve 10⁵ V/T and, therefore, have traditionally been assumed to bethe magnetic field detector of choice. However, the dynamic range of theSQUID is limited to about 10 nT in comparison to 10 μT for singlejunctions. Furthermore, the SQUID transfer function is very non-linear,so to utilize it as a detector it is typically connected to feedbackelectronics that limit the bandwidth to a few MHz.

While progress has been made in the realization of SQUID-based antennas,they are difficult to fabricate because non-uniformity in junctionparameters rapidly degrades performance. An alternative approach isneeded that is simpler, provides greater signal-to-noise ratio andbetter performance and is easier to manufacture.

SUMMARY OF THE INVENTION

In an exemplary embodiment, Josephson junction arrays are used to form asmall transducer capable of converting magnetic flux into voltage. Thistransducer, which may also be referred to as a “Fraunhofer-based device”or “Fraunhofer magnetic field sensor-based” (“FMFS-based”), may be usedas a magnetic antenna, amplifier or magnetometer with very highlinearity, ultra wide bandwidth, large dynamic range and highsensitivity. In general, the inventive approach may be used in anyapplication requiring magnetic field sensing with high linearity andwide bandwidth, including biomedical magnetic imaging and magneticmicroscopes. The device of the invention has improved linearity, dynamicrange and bandwidth compared to the existing art. Furthermore,fabrication of the device is relatively simple and thus suitable forcommercial production. In addition, the device simplifies the supportelectronics necessary for the implementation in various applications.

Using arrays of very large numbers of nano-Josephson junctions willincrease the output voltage and therefore sensitivity. The bestJosephson junctions for this are nano-Josephson junctions fabricatedwith ion beam damage (see K. Chen, S. A. Cybart, and R. C. Dynes, Appl.Phys. Lett. 85, p2863, 2004), because unlike other HTS junctiontechnologies they can be very closely spaced (˜150 nm) (see K. Chen, S.A. Cybart, and R. C. Dynes, IEEE Trans. Appl. Supercond. 15, p149, 2005;and S. A. Cybart, K. Chen and R. C. Dynes, IEEE Trans. Appl. Supercond.15, p241, 2005), positioned anywhere on a substrate and have excellenttemporal stability (see S. A. Cybart et al. IEEE Trans. Appl. Supercond.23, p 1100103, 2013.)

The inventive FMFS-based device uses the Fraunhofer pattern of a 1Darray for converting magnetic flux to voltage by connecting multipleJosephson junctions in a series array. The FMFS-based device uses theintrinsic Josephson junction sensitivity to magnetic fields to produce avoltage that is a highly linear function of the applied magnetic field.The inventive approach uses a single junction or an array of longjunctions in the linear Fraunhofer mode to transduce magnetic fieldsthat are perpendicular to the junction. These magnetic fields can bedirectly coupled from the environment (magnetometer or antenna), coupledthrough a flux transformer element (magnetometer or antenna), or coupledfrom on-chip inductors where the junctions will be used to transduce thecurrent in these inductors to a voltage (current to voltage transducer).

In an exemplary embodiment, the array is lithographically fabricated toform on the order of 10⁶ junctions. In one embodiment, the series, orlinear, array of Josephson junctions may be fabricated on a relativelysmall substrate by configuring it as a meandering line with tens,hundreds, or thousands of meanders. For example, for a 1 cm×1 cm chip,an estimated 400 meanders (25 micron periodicity) with an inter-junctionspacing of 0.5 microns would yield a total of 8×10⁶ junctions. Assuminga typical single junction I_(C)R product of 100 μA×1 Ohms=100 μV and 50%modulation of the critical current to zero, this would yield 400 Volts.If only 25% of this signal has a usable linear range, it would stillyield 100 V/10 μT or equivalently 10⁷ V/T, which is two orders ofmagnitude better than a SQUID with the added benefits of dynamic range,linearity and a bandwidth from DC to GHz.

The general architecture of a FMFS-based device according to theinvention can include anywhere from single long Josephson junction up tomillions of junctions in series. In addition, series-parallel junctionarrays may be used where the Josephson junctions in parallel areconnected in such a way that they do not exhibit SQUID properties, i.e.,large β_(L) factor (β=I₀(2L/Φ₀≥100), large inductance, and/or out ofplane. The SQUID properties can be avoided by using a large enoughinductance connecting the junctions in the parallel direction.

The FMFS-based device exploits the intrinsic Josephson junctionsensitivity to magnetic fields to produce a voltage that is a highlylinear function of applied magnetic field, i.e. the junction Fraunhofer.A key aspect of the invention is the use of a single junction or anarray of long junctions in the linear Fraunhofer mode to transducemagnetic fields that are perpendicular to the junction. These magneticfields can be directly coupled from the environment (magnetometer orantenna), coupled through a flux transformer element (magnetometer orantenna), or coupled from on-chip inductors where the junctions will beused to transduce the current in these inductors to a voltage (currentto voltage transducer).

While the examples described herein refer to YBCO superconductors, theinventive devices may be formed using virtually any superconductingmaterial in which a Josephson junction may be made, including Nb, Pb,Al, MgB₂, cuprates, etc. Any junction barrier-type may also be used,including, but not limited to Superconductor-Insulator-Superconductor(SIS), Superconductor-Normal Metal-Superconductor (SNS), andSuperconductor-diminished superconductor-Superconductor (SS′S). Inaddition, while the exemplary embodiments describe ion damage Josephsonjunctions, the junctions may be formed using any other known method,including, but not limited to SIS trilayer, step-edge junctions,bicrystal junctions, grain boundary junctions, ramp junctions, andothers.

The configuration of the junction array may follow any planar geometry,including lines, spirals, circles, meanders, combinations thereof, orany shape that is appropriate for a specific antenna. The planargeometry may optionally include flux focusing elements, or otherelements such as flux input elements for current-to-voltagetransduction. The device may include any number of elements arranged ina series or parallel relationship. The structures may be resonant ornon-resonant, with the broadest bandwidth being achieved withnon-resonant structures.

In one aspect of the invention, a transducer for converting magneticflux to voltage comprising an array of Josephson junctions disposed in aplanar geometry configured to operate in a linear Fraunhofer mode totransduce magnetic fields that are perpendicular to the junction. Thearray may include from 1 to 10⁹ junctions where the Josephson junctionsare long Josephson junctions, which may have a bridge width within arange of 4-10 μm. In some embodiments, the planar geometry may be ameandering line. Such a meandering line may include from 10 to 10⁶meanders. In other embodiments, the planar geometry may be selected fromlines, spirals, circles, meanders, or combinations thereof. The arraymay be arranged in series, parallel, or series-parallel. The transducermay further comprise a plurality of bond pads in electricalcommunication with the array. In some embodiments, the array ofJosephson junctions is formed from an YBCO superconductor, while inothers the array of Josephson junctions is formed in a superconductingmaterial selected from the group consisting of Nb, Pb, Al, MgB₂, andcuprates. The Josephson junctions may comprise junction barriersselected from the group consisting ofSuperconductor-Insulator-Superconductor (SIS), Superconductor-NormalMetal-Superconductor (SNS), and Superconductor-diminishedsuperconductor-Superconductor (SS′S) with junctions selected from thegroup consisting of ion damage Josephson junctions, SIS trilayers,step-edge junctions, bicrystal junctions, grain boundary junctions, andramp junctions.

In another aspect of the invention, a device for converting magneticflux to voltage comprises a planar array of long Josephson junctionsdisposed on a substrate, where the planar array is configured in ageometry selected from a line, spiral, circle, meandering line, andcombinations thereof and a plurality of contacts disposed on thesubstrate in electrical communication with the planar array. The planararray may include from 1 to 10⁹ junctions. The Josephson junctionswithin the array are long Josephson junctions. In some embodiments, thegeometry is a meandering line having from 10 to 10⁶ meanders. In otherembodiments, the planar geometry may be selected from lines, spirals,circles, meanders, or combinations thereof. The array may be arranged inseries, parallel, or series-parallel. In some embodiments, the array ofJosephson junctions is formed from an YBCO superconductor, while inothers, the array of Josephson junctions is formed in a superconductingmaterial selected from the group consisting of Nb, Pb, Al, MgB₂, andcuprates. The Josephson junctions may comprise junction barriersselected from the group consisting ofSuperconductor-Insulator-Superconductor (SIS), Superconductor-NormalMetal-Superconductor (SNS), and Superconductor-diminishedsuperconductor-Superconductor (SS′S) with junctions selected from thegroup consisting of ion damage Josephson junctions, SIS trilayers,step-edge junctions, bicrystal junctions, grain boundary junctions, andramp junctions.

In another aspect of the invention, a method for converting magneticflux to voltage comprises using a Fraunhofer pattern of a 1D array ofJosephson junctions. The 1D array of Josephson junctions may includefrom 1 to 10⁹ junctions. The Josephson junctions within the array arelong Josephson junctions and may be configured in a planar geometryselected from a line, spiral, circle, meandering line, and combinationsthereof. In some embodiments, the planar geometry is a meandering linehaving from 10 to 10⁶ meanders. The array may be arranged in series,parallel, or series-parallel. In some embodiments, the array ofJosephson junctions is formed from an YBCO superconductor, while inothers, the array of Josephson junctions is formed in a superconductingmaterial selected from the group consisting of Nb, Pb, Al, MgB₂, andcuprates. The Josephson junctions may comprise junction barriersselected from the group consisting ofSuperconductor-Insulator-Superconductor (SIS), Superconductor-NormalMetal-Superconductor (SNS), and Superconductor-diminishedsuperconductor-Superconductor (SS′S) with junctions selected from thegroup consisting of ion damage Josephson junctions, SIS trilayers,step-edge junctions, bicrystal junctions, grain boundary junctions, andramp junctions.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A and 1B are diagrammatic views of short and long Josephsonjunctions depicting current density distribution (prior art).

FIG. 2A is a diagrammatic perspective view of a device constructed witha meandering geometry according to an embodiment of the presentinvention; FIG. 2B is a top plan view of an embodiment of the FMFSdevice; FIG. 2C is a diagrammatic view of an exemplary spiral geometry;FIG. 2D is a diagram of an exemplary double spiral configuration; andFIG. 2E is a diagram of a planar layout with groups of meanders indifferent orientations.

FIG. 3A is a plot showing the Fraunhofer and SQUID pattern for a 10×1000two dimensional SQUID array fabricated with 2 micron wide junctions.;FIG. 3B is a plot comparing the linearity of the Fraunhofer and SQUIDpatterns.

FIG. 4A is an optical micrograph of single junction devices fabricatedwith different bridge widths according to an embodiment of theinvention; FIG. 4B is a diagrammatic view of the device of FIG. 4A.

FIGS. 5A-5G are plots of critical current versus flux demonstrating theevolution of bridge width and the increasingly linear behavior withincreasing bridge width.

FIG. 6A-6D illustrate increasing linearity and skew in the central peakwith increasing bridge width.

FIGS. 7A-7F provide results of a simulation investigating the effects ofcritical current non-uniformity on a long Josephson junction amplifierfor a standard deviation σ=0.05 and 0.10.

FIGS. 8A-8F show results of a simulation investigating the effects oflithographically-defined junction area non-uniformity on a 100 junctionarray for a standard deviation σ=0.05 and 0.10.

FIGS. 9A-9F show results of a simulation combining both the effects oflithographically-defined junction area non-uniformity and criticalcurrent non-uniformity on a long Josephson junction amplifier.

FIG. 10A-10B are plots of the junction period of the magnetic fieldpattern vs. junction width.

FIG. 11 is a plot of junction sensitivity as a function of junctionwidth.

FIG. 12 is a plot showing increased junction linearity with junctionwidth.

FIG. 13 is a diagrammatic view of a wide bridge device according to anembodiment of the invention.

FIG. 14 is a plot of the estimated sensitivity of the wide bridge deviceof FIG. 13.

DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION

A Fraunhofer magnetic field sensor (FMFS)-based device is formed from anarray of Josephson junctions to produce increased voltage yield,improved sensitivity, and signal-to-noise ratio well beyond thatobtainable from SQUID devices. The inventive devices are capable ofoperation above the boiling point of liquid nitrogen, can be verydensely spaced ˜500 nm, easily manufactured, are uniform to better than10% variation with excellent temporal stability. Utilization of widejunctions greatly simplifies photolithography while increasingsensitivity and linearity. The voltage obtainable by large linear arraysaccording to the FMFS junction technology is unsurpassed due to thelarge number of junctions possible.

FIG. 2A diagrammatically illustrates an example of a FMFS-based device10 fabricated on 1 cm×1 cm substrate 16 consisting of a series array 8of Josephson junctions 12 arranged in a meander geometry. Each of thejunctions 12 is a long Josephson junction, i.e., one in which thejunction width is larger than λ_(J) so that the current is concentratedat the edges. (See, e.g., FIG. 1B.) Lines of Josephson junctions 12define a meander leg 20, with pairs of meander legs 20 joined bysuperconducting bridge switch-backs 18. For simplicity in illustration,in FIG. 2A, each meander leg 20 is shown as having ten (10) Josephsonjunctions 12, however, it will be readily apparent to those in the artthat the number of junctions within a meander leg or within the entiremeander structure will be selected based on a number of factorsincluding, but not limited to, fabrication methods and desired devicecharacteristics. Selection of appropriate numbers of junctions,inter-junction spacing, numbers of meanders and their dimensions will bewithin the level of skill in the art based on the examples describedherein. Contacts 14 disposed at the switch-backs 18 and at the meanderends 22 provide for external connection. The contacts 14 may be goldbond pads or other appropriate conductors.

FIG. 2B provides a diagrammatic top view of an embodiment of aFMFS-based device 110 shown with a larger number N of meanders 28, butotherwise configured using with the same basic elements as describedwith reference to FIG. 1B. The meanders may number on orders ofmagnitude of 10 to 10⁶ or more, with junctions numbering from a singlejunction to billions (10⁹) or more, limited only by practicalfabrication constraints, to achieve the desired performance, with thesubstrate size being scaled as needed.

Modestly estimating 400 meanders (25 micron periodicity) with 200switch-backs and an inter-junction spacing of 0.5 microns would yield atotal of 8×10⁶ junctions. Assuming a typical single junction I_(C)Rproduct of 100 μA×1 Ohms=100 μV and 50% modulation of the criticalcurrent to zero, this would yield 400 Volts. If only 25% of this signalhas a usable linear range, it would still yield 100 V/10 μT, orequivalently 10⁷ V/T, which is two orders of magnitude better than aSQUID with the added benefits of dynamic range, linearity and abandwidth from DC to GHz. An additional benefit Fraunhofer devices mayhave over SQUID devices is lower noise properties.

The general architecture of a FMFS-based device according to theinvention can include anywhere from single long Josephson junction up tomillions of junctions in series. In addition, series-parallel junctionarrays may be used where the Josephson junctions in parallel areconnected in such a way that they do not exhibit SQUID properties, i.e.,large β_(L) factor (β=I₀(2L/Φ₀≥100), large inductance, and/or out ofplane. (See, e.g., Tesche and Clarke, J. Low Temp. Phys., Vol. 29, No.3/4, 1977.) The SQUID properties can be avoided by using a sufficientlylarge inductance connecting the junctions in the parallel direction.

While the examples described herein refer to YBCO (YBa₂Cu₃O_(7-δ))superconductors, the inventive devices may be formed using virtually anysuperconducting material in which a Josephson junction may be made,including Nb, Pb, Al, MgB2, cuprates, etc. Any junction barrier-type mayalso be used, including, but not limited toSuperconductor-Insulator-Superconductor (SIS), Superconductor-NormalMetal-Superconductor (SNS), and Superconductor-diminishedsuperconductor-Superconductor (SS′S). In addition, while the exemplaryembodiments describe ion damage Josephson junctions, the junctions maybe formed using any other known method, including, but not limited toSIS trilayer, step-edge junctions, bicrystal junctions, grain boundaryjunctions, ramp junctions, and others.

Appropriate configurations of the planar array of Josephson junctionsextend far beyond the meandering line geometry described in theexemplary embodiment. The configuration of the junction array may followany planar geometry, including lines, spirals, circles, meanders,combinations thereof, or any shape that is appropriate for a specificantenna. FIGS. 2C-2E illustrate a few possible planar geometryconfigurations, showing a spiral (FIG. 2C), a double spiral (FIG. 2D) orgroups of meanders in different orientations (FIG. 2E). Many otherconfigurations are possible. The planar geometry may optionally includeflux focusing elements, or other elements such as flux input elementsfor current-to-voltage transduction. The device may include any numberof elements arranged in a series or parallel relationship. Thestructures may be resonant or non-resonant, with the broadest bandwidthbeing achieved with non-resonant structures.

With regard to the junction spacing, there is no limit to the spacingfor the invention described. For any given junction technology, anyrange of spacings that can produce Josephson junctions will be withinthe scope of the invention. The highest density of junctions is set bythe practical fabrication limits. For a high voltage output in a smallarea, a high density junction technology is most desirable. For improvedcoupling of the device to external HF fields, a large area is desirable.For an RF device, a distributed array of a limited number of junctionsis preferred. For example, with 1 Ohm junctions matching a 50 Ohm load,radio frequency power is most efficiently transduced for approximately50 junctions rather than millions.

The inventive FMFS-based device uses the Fraunhofer patterns of a 1Darray in contrast to a 2D array used in a SQUID array. FIG. 3A shows themagnetic field response of a 2D 10×1000 junction array (SQUID array).Josephson junctions exhibit both interference and diffraction. Smalloscillation (quantum interference) from the SQUID areas and largeoscillation (quantum diffraction) are determined by the junction area.The sharp Fraunhofer modulation of the SQUID transfer function is anindicator that the junctions have uniform areas and critical currents. A1D array exhibits only the Fraunhofer pattern, which is far more linearthat the SQUID pattern and has a dynamic range that is about 1,000 timeslarger. FIG. 3B illustrates how the Fraunhofer regime (upper line—1×200junction array) is very linear compared to a SQUID array (lowerline—5×1000 junction array) while having a much larger dynamic range.(Note that the upper axis scale (in μT) corresponds to the SQUID patternwhile the lower axis scale (in mT) corresponds to the Fraunhoferpattern, as indicated by the double arrows.) To achieve the samesensitivity as a SQUID, it is simply a matter of increasing the numberof junctions to scale up the voltage.

Using photolithographic processes an array comprising a large number (onthe order of hundreds to multiple millions) of Josephson junctions isformed on a substrate. The FMFS devices may be fabricated by a number ofdifferent process, including conventional photolithographic processes asare known in the art, and the photolithographic processes described byS. A. Cybart, et al. in “Very Large Scale Integration of NanopatternedYBa₂Cu₃O_(7-δ) Josephson Junctions in a Two-Dimensional Array”,Nanoletters, 2009, Vol. 9, No. 10, 3581-3585, which is incorporatedherein by reference.

Briefly, the process described by Cybart, et al., involves the steps ofthermal co-evaporation of a superconducting, e.g., YBCO, thin film on asapphire wafer followed by deposition of a gold contact layer. The filmsare patterned using photolithography and argon ion (Ar⁺) milling tofabricate a microstrip. The gold layer over the junctions was removedusing a subsequent photolithography step and chemical gold etch, leavingthe contact pads. The junctions are fabricated by coating the wafer witha layer of photoresist, which is then hardbaked, to serve as the primaryion stopping layer. A thin (e.g., 25 nm) layer of germanium (Ge) may beelectron-beam evaporated on top of the resist to also serve as an etchstop. A layer of poly(methyl methacrylate) (PMMA) resist is spun ontothe Ge layer for electron-beam lithographic patterning. Using an e-beamwriter, such as a 100 keV Leica VB6-HR nanowriter, or similarconventional e-beam system, lines are written into the PMMA over thelocations intended for the junctions. This pattern is transferred intothe Ge layer by reactive ion etching (RIE) in a HBr—Cl₂ plasma etcher.The pattern in the Ge is transferred to the resist using low temperature(˜−100° C.), low pressure (5 mTorr) oxygen RIE. Following etching, thewafers are implanted to induce ion damage in the areas not protected bythe mask. The implant dose will depend on the desired junctionparameters.

An alternative fabrication method is disclosed in co-pendingInternational Application No. PCT/US2015/035426, filed Jun. 11, 2015,which is incorporated herein by reference. The process is also describedby S. A. Cybart, et al., in “Nano Josephson superconducting tunneljunctions in YBa₂Cu₃O₇₋₆₇ directly patterned with a focused helium ionbeam”, Nature Nanotechnology, 2015, 10(598-602), published on-line 27Apr. 2015.

FIG. 4A is an optical micrograph taken at 2× magnification of a testsample chip with FMFS-based devices fabricated from YBCO strips ofvarying bridge widths. FIG. 4B provides a diagrammatic view of the samestructure, with the bridge widths indicated. As previously described,bridge width W impacts to Josephson penetration depth, determiningwhether the junction is considered “long” or “short.” The actualjunctions are too small to be seen in the photographic image, but areindicated by the black “Xs. In FIG. 4B, the junctions are illustrated asthe light gray areas in the centers of the wider strips (not shown inthe narrower strips.) The devices 30-39 have bridge widths W of 50 μm,30 μm, 15 μm, 10 μm, 8 μm, 6 μm, 5 μm and 4 μm, from top to bottom ofthe image. Bond pads 14 are shown in both images, with the voltage andcurrent connections for the 50 μm bridge indicated in FIG. 4B.

FIGS. 5A-5G provide the results of the evaluation of bridge width andits impact on device response. FIG. 5A shows the critical current versusflux pattern for a 2 μm bridge width at a temperature of 4K. FIG. 5B isa plot of critical current versus flux for a 3 μm bridge width at atemperature of 4K. FIGS. 5C and 5D are plots of critical current versusflux for a 4 μm bridge width at 4K and 77K, respectively. FIG. 5E showsthe pattern for a 6 μm bridge width at 80K. FIG. 5F provides the resultsof an 8 μm bridge at 80K. FIG. 5G provides the results for a 10 μmbridge at 80K. The Josephson penetration depth for this set ofexperiments is around 3˜4 μm. Looking at the evolution of the patterns,it can be seen that the degree of roundness of the center peaksdiminishes (i.e., becomes sharper) as bridge width increases. For bridgewidths greater than 6 μm, the curves in the pattern are replaced by alinear slope. The shape of the pattern is the most important, becausethe sensitivity and the dynamic range can be adjusted by the number ofjunctions in series. What is demonstrated by these results is that theshorter junctions have a round center peak whereas in the longerjunctions, the center peak transitions to a triangle. The increasedsharpness of the slope with increasing bridge width corresponds togreater sensitivity due to the larger area (Φ=BA). It should be notedthat the data were obtained using different devices. Also, the operatingtemperature can be tuned anywhere within a range of 4K to 80K.

FIGS. 6A-6D provide an additional example of how linearity and skew inthe central peak increase with increasing bridge width. Single junctionswith bridge widths of 4, 6, 8 and 10 μm were tested at 77K, with theresults plotted in FIGS. 6A-6D, respectively. Devices larger than 10microns did not function properly because the width became too large.

A close-spaced series array with 1000 meanders, 10 μm bridge width, and100 nm junction spacing fabricated on a 1 cm×1 cm area chip wouldproduce a device having 10⁹ junctions. Using the results shown in FIG.6D, the I_(C)R product for a single junction (250 μA×0.13Ω) would be32.5 μV. Modulation of the critical current to zero (a change inmagnetic field of 35 μT) for a single junction corresponds to ˜1 V/T,which, for 10⁹ junctions produces 1 V/nT.

To investigate the effects that non-uniform critical currents might haveon the linearity and dynamic range of such an array, we simulated alinear array of I_(C)(B) patterns by summing the voltages of triangularshaped functions of different amplitudes for both a 0.10 and 0.05critical current standard deviation. FIG. 7A illustrates thevoltage-flux characteristic of each junction for σ=0.05, FIG. 7B showsthe results for each junction for σ=0.10. For all junctions summed, theresults are shown in FIGS. 7C and 7D for σ=0.05 and 0.10, respectively.FIGS. 7E and 7F plot the slopes of all junctions for σ=0.05 and 0.10,respectively. Based on these results, there appeared to be little or noeffect on range or linearity for either case. Our current junctions havebeen demonstrated with standard deviations in critical current of around0.12. To simulate variation in junction area, triangles of differentperiodicity were evaluated for a 100 junction array. The results,provided in FIGS. 8A-8F, indicate that linearity is not affected anddynamic range is only slightly reduced for a 0.10 standard deviation injunction area compared to 0.05. As in the previous simulation, FIGS. 8Aand 8B show the voltage-flux characteristic for each junction for avariation in junction area of σ=0.05 and 0.10, respectively, FIGS. 8Cand 8D provide the characteristic for the sum of all 100 junctions forσ=0.05 and 0.10, and FIGS. 8E and 8F provide the slope of all junctionsfor σ=0.05 and 0.10, respectively.

The effect of a combination of variations in both effects (criticalcurrent non-uniformity and junction area variation) on a long Josephsonjunction amplifier is demonstrated in the simulation results shown inFIGS. 9A-9F. Area variation is determined by lithographic error (whichis very small, especially for long junctions) to be ˜0.02 standarddeviation from the mean area. The derivative shows a very smallreduction in dynamic range, which can easily be compensated for byadding more junctions. FIGS. 9A and 9B show the voltage-fluxcharacteristics for each junction for a variation in junction area ofσ_(A)=0.05 and 0.10, and a variation in critical current of σ_(I)=0.10and 0.20, respectively. FIGS. 9C and 9D provide the characteristics forthe sum of all 100 junctions for σ_(A)=0.05 and 0.10, and σ_(I)=0.10 and0.20. FIGS. 9E and 9F provide the slope of all junctions for σ_(A)=0.05and 0.10, and σ_(I)=0.10 and 0.20, respectively.

FIG. 10A-10B are plots of the junction period of the magnetic fieldpattern vs. junction width, demonstrating how larger bridge widthsubstantially reduces the field period and, hence, increasessensitivity. The upper line in each plot is proportional to 1/w², wherew is the bridge width.

Sensitivity can be defined as the slope of the magnetic field patternoperated in voltage mode dV/dB. To evaluate sensitivity, the device isbiased with a static current above the critical current and voltage isdetected. In FIG. 11, sensitivity is plotted as a function of junctionwidth, demonstrating that sensitivity increases with width.

The linearity of a device can be analyzed by fitting a straight line(IcB) from the center peak to the first minimum of the steeper side anddetermining the residual sum of squares from the fit. As shown in FIG.12, the residual sum of squares of each fit decreases as the junctionwidth increases, indicating improved linearity with increasing width.

From these above-described tests, we learned that using a wider bridgegives greater sensitivity, however the junction should be 10 μm or less.Therefore, one approach for an optimized device is to create a junctioncontained inside of a much larger bridge. FIG. 13 illustrates an exampleof a 50 μm wide bridge with an approximately 10 μm junction inside. Tobuild this, on substrate 50, we use a low ion dose to write the junction54 and a very large dose to write insulating barriers 52 on the sides.The area within the dashed lines 56 corresponds to the effectivejunction area. FIG. 14 is a plot of the estimated sensitivity of thewide bridge device of FIG. 13 for bridge widths ranging from 4 μm up to100 μm for a constant 6 μm junction width, where the junction period(left axis) is plotted against bridge width as indicated by the blackdots, and junction sensitivity (right axis) is plotted against bridgewidth, indicated by the black squares.

Using the approaches described herein, a device for converting magneticflux to voltage can be fabricated on a small substrate using relativelystraightforward lithographic processes. A FMFS-based transducer can beused as a magnetic antenna, amplifier, magnetometer, magnetic fieldsensor or for satellite communication with very high linearity, ultrawide bandwidth, large dynamic range and high sensitivity. Such a deviceprovides significant advantages over existing SQUID-based technologiesbecause it is simpler and more easily commercialized. A significantadditional advantage lies in the fact that the supporting electronicsrequired for implementation of an FMFS-based antenna, amplifier and/or amagnetometer are greatly simplified relative to existing SQUID-basedtechnologies. The inventive approach describe above is not limited toantenna-like applications, but may be used in any application requiringmagnetic field sensing with high linearity and wide bandwidth, includingbiomedical magnetic imaging and magnetic microscopes.

References (incorporated herein by reference):

1. V. Martin et al., “Magnetometry based on sharpened high Tc GBJFraunhofer patterns”, IEEE Trans. Appl. Supercond. 7(2):3079-3082, 1997.

2. J. Clarke and A. Braginski (Eds.), The SQUID Handbook: Fundamentalsand Technology of SQUIDs and SQUID Systems, Volume I, and The SQUIDHandbook: Applications of SQUIDs and SQUID Systems, Volume II, Wiley-VCHVerlag GmbH & Co., 2006.

3. A. V. Shadrin, et al., “Fraunhofer regime of operation forsuperconducting quantum interference filters”, Appl. Phys. Lett.93(26):262503, 2008.

4. C. D. Tesche and J. Clarke, “dc SQUID: Noise and Optimization”, J.Low Temp. Phys., 29(3/4):301-331, 1977.

5. K. Chen, et al., “Planar thin film YBa₂Cu₃O_(7-δ) Josephson junctionpairs and arrays via nanolithography and ion damage”, Appl. Phys. Lett.85(14): 2863-2865, 2004.

6. K. Chen, et al., “Study of closely spaced YBa₂Cu₃O_(7-δ) Josephsonjunction pairs”, IEEE Trans. on Appl. Supercond., 15(2):149-152, 2005.

7. S. A. Cybart, et al., “Planar YBa₂Cu₃O_(7-δ) ion damage Josephsonjunctions and arrays”, IEEE Trans. on Appl. Supercond., 15(2): 241-244,2005,

8. S. A. Cybart et al., “Temporal Stability of Y—Ba—Cu—O Nano JosephsonJunctions from Ion Irradiation,” IEEE Trans. on Appl. Supercond., 23(3):1100103, 2013.

9. S. A. Cybart, et al. “Very Large Scale Integration of NanopatternedYBa₂Cu₃O_(7-δ) Josephson Junctions in a Two-Dimensional Array”,Nanoletters, 2009, 9(10): 3581-3585.

10. S. A. Cybart, et al., “Nano Josephson superconducting tunneljunctions in YBa₂Cu₃O_(7-δ) directly patterned with a focused helium ionbeam”, Nature Nanotechnology, 2015, 10 (598-602), 27 Apr. 2015.

The invention claimed is:
 1. A method for converting magnetic flux tovoltage comprising using a one-dimensional planar array of longJosephson junctions on a substrate, wherein the planar array isconfigured in a geometry selected from line, spiral, circle, meanderingline, and combinations thereof, wherein each long Josephson junction hasa bridge width greater than two times the Josephson penetration depth.2. The method of claim 1, wherein the planar geometry comprises ameandering line comprising from 10 to 10⁶ meanders.
 3. The method ofclaim 1, wherein the array of Josephson junctions comprises from 1 to10⁹ junctions.
 4. The method of claim 1, wherein the Josephson junctionshave a bridge width within a range of 4 to 100 μm.
 5. The method ofclaim 4, wherein the Josephson junctions have a junction width muchnarrower than the bridge width.
 6. The method of claim 1, wherein theJosephson junctions have a bridge width within a range of 4 to 10 μm. 7.The method of claim 1, wherein the array is arranged in series,parallel, or series-parallel.
 8. The method of claim 1, wherein thearray of Josephson junctions is formed from an YBCO superconductor. 9.The method of claim 1, wherein the array of Josephson junctions isformed in a superconducting material selected from the group consistingof Nb, Pb, Al, MgB₂, and cuprates.
 10. The method of claim 1, whereinthe Josephson junctions comprise junction barriers selected from thegroup consisting of Superconductor-Insulator-Superconductor (SIS),Superconductor-Normal Metal-Superconductor (SNS), andSuperconductor-diminished superconductor-Superconductor (SS′S).
 11. Themethod of claim 1, wherein the Josephson junctions comprise a junctionselected from the group consisting of ion damage Josephson junctions,SIS trilayers, step-edge junctions, bicrystal junctions, grain boundaryjunctions, and ramp junctions.
 12. A method for converting magnetic fluxto voltage comprising using a Fraunhofer pattern of a 1D array of longJosephson junctions.
 13. The method of claim 12, wherein the ID array oflong Josephson junctions is configured in a planar geometry selectedfrom line, spiral, circle, meandering line, and combinations thereof.14. The method of claim 12, wherein the array comprises from 1 to 10⁹long Josephson junctions.
 15. The method of claim 12, wherein theJosephson junctions have a junction width much narrower than the bridgewidth.
 16. The method of claim 12, wherein the junction width is lessthan 10 μm and the bridge width is in a range of 50 to 100 μm.
 17. Themethod of claim 12, wherein the array is arranged in series, parallel,or series-parallel.
 18. The method of claim 12, wherein the array ofJosephson junctions is formed in a superconducting material selectedfrom the group consisting of Nb, Pb, Al, MgB₂, and cuprates.
 19. Themethod of claim 12, wherein the Josephson junctions comprise junctionbarriers selected from the group consisting ofSuperconductor-Insulator-Superconductor (SIS), Superconductor-NormalMetal-Superconductor (SNS), and Superconductor-diminishedsuperconductor-Superconductor (SS′S).
 20. The method of claim 12,wherein the Josephson junctions comprise a junction selected from thegroup consisting of ion damage Josephson junctions, SIS trilayers,step-edge junctions, bicrystal junctions, grain boundary junctions, andramp junctions.